The model-based reconstruction of electrical brain activity from electroencephalographic measurements is of constantly growing importance in the fields of Neurology and Neurosurgery. Algorithms for this task involve the solution of a 3D Poisson problem on a complicated geometry and with non-continuous coefficients for a considerable number of different right hand sides. Thus efficient solvers for this subtask are required. We will report on our experiences with different iterative solvers, Successive Overrelaxation, (Preconditioned) Conjugate Gradients, and Algebraic Multigrid, for a discretisation based on cell-centred finite-differences.